HOUSTON (AP)-Houston's Case Keenum had just thrown his fifth touchdown pass against Rice to set the Football Bowl Subdivision record for career TD tosses and coach Kevin Sumlin was asking the officials to give him the ball.

They didn't hear him and the record-setting ball sailed into the stands as Houston kicked the extra point.

Sumlin was relieved as he watched the fan who caught it throw it back onto the field so he could present it to his quarterback after the game.

Keenum didn't slow down after that, finishing with a career-high nine TD passes as the 18th-ranked Cougars overcame a slow start in a 73-34 win over Rice on a rain soaked Thursday night.

"I bet if the fans knew that was the ball, we wouldn't have got it back," Sumlin said. "That was very, very nice. I'd like to thank our fans for getting that ball back."

Keenum threw an interception and had a fumble returned for a touchdown in the first quarter in heavy rain as Rice built a 17-7 lead.

With the rain at its heaviest, Sumlin expressed his disbelief at the weather into his headset.

"I said: 'Surely it's not going to be like this all night. It can't rain like this all night," he said. "I guess somebody heard me because it started to stop after that."

Then the Cougars got going. They outscored Rice 45-3 to take a 52-20 lead by early in the third quarter and cruised to the easy victory to remain undefeated.

Keenum, who became the FBS career leader in total offense last week, has 139 career touchdown passes.

Tyler Smith had 170 yards rushing and two rushing and one receiving touchdown for Rice (2-6, 1-4). That included a 97-yard scoring run which was the longest TD run in school history.

"(Keenum) made plays every time they had to, and we couldn't make plays that we needed to stop them," Rice coach David Bailiff said. "We had some opportunities but didn't get it done."

The Owls were ahead 17-7 late in the first quarter before Keenum threw his first touchdown pass for 57 yards to Edwards. The teams exchanged field goals at the beginning of the second quarter to leave Rice up 20-17.

Keenum then threw three touchdown passes in a six minute span at the end of the first half to put Houston on top 38-20 and tie the touchdown passes record.

He set the record on a 41-yard pass to Charles Sims early in the third quarter to push the lead to 45-20. Keenum smiled and flashed the Cougar hand signal when he appeared on the jumbotron on the sidelines after setting the record. His teammates clapped and cheered while fans gave him a standing ovation.

He was 24 of 37 for 534 yards before he was replaced by backup Cotton Turner with eight minutes remaining.

"Those are video game numbers, something we couldn't get stopped," Rice linebacker Justin Allen said of Keenum's performance. "The rain slowed down a little bit. I wished it would have rained all game. It stopped, and they got things cranked up. There was no looking back for them."

Keenum, who was granted a sixth year of eligibility after tearing a knee ligament early last season, needs 267 yards passing to become the FBS's all-time leader in passing yards which is held by Hawaii's Tim Chang (17,072).

Tyron Carrier tied the NCAA record for career kickoff returns for touchdowns with seven by returning the opening kickoff 100 yards for a score. Carrier dashed down the right sideline and darted around the defense virtually untouched before outrunning the kicker for the score.

Actually, Carrier said no one got a finger on him on the return.

"Not a touch," he said. "That's the way it should be."

He shares the record with C.J. Spiller of Clemson who had seven kickoff returns for touchdowns from 2006-09.

Carrier also had a touchdown reception, Sims had two and Justin Johnson added one for the Cougars.

Rice made it 7-3 with a 51-yard field goal by Chris Boswell early in the first quarter.

The Owls used a squib kick on the ensuing kickoff to keep the ball away from Carrier and defensive lineman Austin Lunsford fielded it and fumbled and Rice recovered.

Rice took advantage of the miscue on a 1-yard touchdown run by Smith that made it 10-7.

With the rain coming down at its heaviest, Houston couldn't get its offense going early and had to punt after Rice went ahead. The Cougars next possession ended when Keenum was intercepted by Bryce Callahan.

The Owls came up empty on the ensuing drive when Boswell slipped on the rain-slicked grass and missed a 38-yard field goal attempt.

The wet conditions continued to be a factor on Houston's next drive when the wet ball slipped out of Keenum's hand as he tried to pass. Cameron Nwosu scooped it up and ran 12 yards for a touchdown to push Rice's lead to 17-7.

The rain had let up when Houston got the ball back and Keenum found Edwards for his first touchdown pass.